Problem: Rewrite as a simplified fraction. ${0.8\overline{6} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 86.6666...\\ 10x &= 8.6666...\end{align*}}$ Subtracting the two equations, we have: ${90x = 78}$ ${x = \dfrac{78}{90}} $ ${x = \dfrac{13}{15}} $